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Apr
8
answered There exists two of them such that their difference is divisible by --(n)--
Apr
8
comment if $f(x)$ is continuous on $0$ then $x f(x)$ differentiable on $0$
No. why do you think so?
Apr
8
revised if $f(x)$ is continuous on $0$ then $x f(x)$ differentiable on $0$
added 21 characters in body
Apr
8
answered Intuition behind Descartes' Rule of Signs
Apr
8
comment Identity for fractional summation
Without any common property of the $y_i$ you won't have luck. But fortunately, divisions don't accumulate rounding errors (but the addition does).
Apr
8
comment Is continuity preserved under Max operator and Euclidean norm?
The composition of ocntinuous functions is continuous.
Apr
8
revised A number field from the series for $e$
added 2 characters in body
Apr
8
comment A number field from the series for $e$
The original question had $d\colon\mathbb N\to\{0,1\}$ instead of $d\colon\mathbb N\to[0,1]$, which makes a huge difference (with the interval, clearly $[0,1]\subseteq E$).
Apr
8
answered A number field from the series for $e$
Apr
8
comment A number field from the series for $e$
Where's the number field hidden in this question?
Apr
8
comment How does predicate logic handle contradictory statements about something that does not exist?
Also, 3 does not in any way contradict 2.
Apr
8
comment How does predicate logic handle contradictory statements about something that does not exist?
And $\neg\exists p$ is not well-formed.
Apr
8
comment Proof in Graph Theory
The proof depends on the property. And if all have four neighbours - is the graph rolled to a torus?
Apr
8
comment Is it possible that the zeroes of a polynomial form an infinite field?
I assume that the polynomial map $F^n\to K$ is considered.
Apr
8
answered Is it possible that the zeroes of a polynomial form an infinite field?
Apr
8
comment Continuity of the sum of continuous functions
One could replace the first bullit point with continuity of the diagonal map $\Delta\colon X\to X\times X$, $x\mapsto (x,x)$. Then $f+g = (+)\circ(f\times g)\circ \Delta$. For the continuity of $\Delta$, the preimage of a basic open set $U\times V$ is $U\cap V$, hence open.
Apr
7
comment if B is a maximal linearly independent set in V then B is a basis for V
Remark: In the last step we divide by $\alpha_{n+1}$ of whic we only know that it is nonzero. This is where the difference between vector spaces over fields and modules over rings arises (with respect to existence of bases).
Apr
7
answered Let $R$ be a ring with $10$ elements, show that $R$ is commutative.
Apr
7
answered Cauchy sequences are bounded?!
Apr
7
answered An irreducible polynomial cannot share a root with a polynomial without dividing it